Wednesday, July 05, 2006

Dorr is interested in how nominalists can account for the necessity of the claim:

(D) Whenever x is an electron, and y is a duplicate of x (or y is qualitively indiscernible from x, if you think that being a electron is non-intrinsic) then y is an electron.

He first discusses what he calls the physical strategy. The idea is that a science adequate to completely describe the actual world will provide us with the resources to give a real definition of 'duplicate':

(P) For x to be a duplicate of y is for it to be the case that x is an electron iff y is an electron, and x is a quark iff y is a quark, etc...

Unsurprisingly, this suggestion is deemed implausible, since it ignores the possibility of things being duplicates in virtue of sharing alien properties (nominalistically construed, obviously).

What surprised me was that Dorr suggested that our very own Joseph Melia might be a proponent of the physical strategy. This isn't how I understand Joseph's position, and is fairly straightforwardly and obviously inconsistent with the appeals to the possibility of alien properties that he and Divers make in the Analytic Limits paper, etc, so I was interested in why Dorr might have come to think this. I guess he must be going on the remarks on p 8 of Joseph's Truthmaking paper, where he talks about fundamental science being incomplete. Before that he has given solely actual world examples ('charged', 'square', 'mass'), but then, it is pretty hard to give examples of particular alien properties. And he seems to be restricting discussion to moderately sparse properties. But I don't see anything to motivate the idea that there is an implicit restriction to actually instantiated properties. On the contrary, Joe seems often to be pressing the idea that the sensible nominalist should be happy if he can establish that we can see how a certain sentence might be made true, or how the world could be a certain way in virtue of certain of its more fundamental aspects (e.g. why "it could have been the case that there were sets of duplicate objects that were ways that no actual things are" is true) without there being universals, even though we can't actually give a nominalistic paraphrase of the sentence. (This is something that Dorr himself seems to be happy with - he only requires 'paraphrase in principle', though one wonders whether even that may be too strong). That idea obviously carries over neatly to the aliens case. Once we see what is the truth of the sentences about non-alien duplicates consist in, it's not difficult to get a sense of what is explaining the truth of sentences about alien duplicates. And nothing which is illegitimate by the nominalist's lights seems to need brought in.

If it is the remarks on page 8 that is motivating Dorr's characterisation, I think that's a misreading. All Joe seems to be doing there is motivating the idea that we can recognise good truthmaker explanations even in the absence of paraphrase. That's something that ought to carry over very straightforwardly to the aliens case. Dorr notes that there have been 'few explicit defences' of the physical strategy, but suggests despite this, it is quite popular. I think it might be at least a little less popular than he suggests.

Just a reminder that we're looking at Cian Dorr's 'There are no abstract objects' this Friday in the CMM seminar (9.30-11, CETL Building) . I read it last night, and it's well worth a look at. There will be a lot to talk about, but I thought I might just start us off here.

Dorr is interested in nominalist paraphrases of claims that, on the surface, seem to commit us to abstract objects. (The paraphrases can be of the only-possible-in-principle, perhaps-only-with infinitary-resources, variety). He discusses 'modalised' nominalist paraphrases e.g.

(1) The number of the planets is nine

mapping to

(2) If there were (enough) numbers, and the concrete world were just as it is, then the number of the planets would be nine.

He compares (1) and (2) with e.g.

(3) The things that explain the facts about the motion of atoms are subatomic particles of kinds K related to atoms in way W

mapping to

(4) It is consistent with the facts about the motion of atoms that: the things that explain the motion of atoms are subatomic particles of kinds K related to atoms in way W.

(I've modified Dorr's phrasing slightly, but not anything of substance, I hope).

2 and 4 seem to drop the ontological commitments of 1 and 3 respectively. The nominalist obviously likes this in the case of 1 -> 2. But qua scientific realist, he may be less comfortable in being pressured to retreat from 3 to the more cautious, less commital 4. But how can he justify this difference in attitude to 'ontological retreat'?

Obviously there's a lot which could be said here. Dorr points out that whereas both 2 and 4 can be seen as applying complex modal operators to the original sentences 1 and 3, the character of these operators differ. In the case of the nominalist's counterfactual operator, we plausibly have a universal quantifier over worlds:

5) In all worlds (if (enough) numbers exist and the concrete world were just as it is -> the number of the planets is nine)

In the case of the scientific 'cautious man', the consistency claim is plausibly an existential quantifier over worlds:

6) There is a world at which (the things which explain the (actual) motion of atoms are subatomic particles of kind K related to atoms in way W)

Dorr argues that this is an epistemologically important difference, which can help provide a non-ad hoc reason for the nominalist to engage in one kind of ontological retreat, but not another.

What I don't understand is how that helps with the case of e.g.

(4*) If there were subatomic particles of kind K related to atoms in way W, the things that explained the motion of atoms would be subatomic particles of kind K related to atoms in way W.

which is more directly analoguous to (2).

Presumably Dorr must be thinking that there could be subatomic particles of kind K related to atoms in way W without those being the things that explained the motion of atoms. Perhaps there could be e.g. different laws, or there could be some extra things around in some worlds, not of kind K, that also help explain the motion. But everything seems to hang on what gets packed into W. If W includes specification of the relevant laws, and also e.g. that the K-particles + laws completely explain the motion of the atoms, etc, then 4* starts looking true to me. But it shares the logical structure of the nominalist paraphrase, while being non-scientific-realist in spirit.

Am I missing something? Can anybody think of a plausible story on which 4* comes out false, even if a lot is built into W?

This year's Royal Institute of Philosophy Conference - on 'Being' - is being held at Leeds in September. Speakers include Helen Beebee, Kit Fine, John Hawthorne, Jonathan Lowe, Hugh Mellor, Ted Sider and Dean Zimmerman. More details available here